You're right XTRMN8, except that the Omega (and so too the same car in the US, the Cadillac Catera) are a fair whack smaller than a Commodore.
The whole car from the outside looks dimensionally identical to the Commdore. However, put the two side by side and you'll notice the main difference - the size. In particular, that panel up above the rear wheel on the Commodore looks particularly 'slab sided', and the wheelbase makes the commodore look like a cat ready to pounce.
Both the Omega and the Catera don't have that wide-footed stance. So it's more than a cut-and-shut job. The doors, for instance, on the Omega/Catera don't sag and bounce around like the Commodore, a result of the resizing. And there's no way you'd fit the 3.8 in there, let alone an LS1. The biggest engine in the Omeag/Catera is a 3.0L V6.
Having said all that, on that recent test-drive that Skaife did with an HSV, a BMW and a Merc at Nurburgring, all the Germans thought they were dealing with a protoype Omega for the DTM.
The design of the car has been copied, the design of the suspension has been copied. All the engines are imported.
But from that point on, much of the rest of the car is Australian Made. And even as a Ford fan, when you go overseas as an Aussie, suddenly you become proud of the Commodore too.